control: K8 is biplanar (explicit split found by B&B) and needs 8 colours


control: Sulanke's 9-chromatic biplanar graph; explicit split found by B&B


only corridor survivor of K_a + C_b for a>=7 (counting: a=7 -> b<=4.5 -> b=3; a>=8 -> none); K10 contains K9 so it is not biplanar (thickness monotone; theta(K9)=3, Beineke-Harary). Family closes on paper.


m'=3m+n=161 > 6n'-12=126: infeasible. General: a 9-chromatic base contains a 9-critical H with m_H >= 4n_H (min degree 8), so M(H) has m' >= 13n_H > 12n_H - 6 = 6n'-12 always. The plain Mycielskian of ANY 9-chromatic graph overshoots the ceiling; family closes on paper.


chi=6 via SAT (DSATUR ub 6, clique 6); fattest colour class has 3 vertices [0, 7, 8] - merge targets for the next mutation


chi=6 via SAT (DSATUR ub 6, clique 6); fattest colour class has 3 vertices [4, 6, 7] - merge targets for the next mutation


chi=6 via SAT (DSATUR ub 7, clique 6); fattest colour class has 3 vertices [1, 4, 11] - merge targets for the next mutation


chi=6 via SAT (DSATUR ub 6, clique 6); fattest colour class has 3 vertices [0, 5, 11] - merge targets for the next mutation


chi=6 via SAT (DSATUR ub 6, clique 6); fattest colour class has 4 vertices [2, 4, 7, 9] - merge targets for the next mutation


chi=6 via SAT (DSATUR ub 6, clique 6); fattest colour class has 3 vertices [1, 9, 12] - merge targets for the next mutation


chi=7 via SAT (DSATUR ub 7, clique 7); fattest colour class has 3 vertices [0, 11, 13] - merge targets for the next mutation


chi=6 via SAT (DSATUR ub 6, clique 6); fattest colour class has 3 vertices [0, 9, 11] - merge targets for the next mutation


chi=7 via SAT (DSATUR ub 7, clique 7); fattest colour class has 3 vertices [5, 7, 9] - merge targets for the next mutation


chi=6 via SAT (DSATUR ub 6, clique 6); fattest colour class has 4 vertices [8, 11, 12, 13] - merge targets for the next mutation


chi=6 via SAT (DSATUR ub 6, clique 6); fattest colour class has 4 vertices [2, 5, 7, 14] - merge targets for the next mutation


chi=7 via SAT (DSATUR ub 7, clique 7); fattest colour class has 3 vertices [0, 9, 14] - merge targets for the next mutation


chi=7 via SAT (DSATUR ub 7, clique 7); fattest colour class has 3 vertices [0, 14, 15] - merge targets for the next mutation


chi=6 via SAT (DSATUR ub 6, clique 5); fattest colour class has 4 vertices [2, 9, 10, 12] - merge targets for the next mutation


chi=7 via SAT (DSATUR ub 7, clique 7); fattest colour class has 3 vertices [0, 4, 7] - merge targets for the next mutation


layer 2 inserts into the face minimizing collisions with layer 1

collision-avoiding layer 2: m=57 of ceiling 66; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [5, 9, 12]


collision-avoiding layer 2: m=59 of ceiling 66; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [0, 6, 11]


collision-avoiding layer 2: m=61 of ceiling 66; chi=6=omega tracks the clique (DSATUR ub 6); fattest class [0, 8, 11]


collision-avoiding layer 2: m=66 of ceiling 72; chi=8=omega tracks the clique (DSATUR ub 8); fattest class [0, 9]


collision-avoiding layer 2: m=65 of ceiling 72; chi=8=omega tracks the clique (DSATUR ub 8); fattest class [0, 9]


collision-avoiding layer 2: m=64 of ceiling 72; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [0, 7]


collision-avoiding layer 2: m=70 of ceiling 78; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [0, 10, 14]


collision-avoiding layer 2: m=72 of ceiling 78; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [2, 10, 14]


collision-avoiding layer 2: m=73 of ceiling 78; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [3, 9, 14]


collision-avoiding layer 2: m=80 of ceiling 84; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [0, 4, 13]


collision-avoiding layer 2: m=77 of ceiling 84; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [2, 12, 14]


collision-avoiding layer 2: m=80 of ceiling 84; chi=8=omega tracks the clique (DSATUR ub 8); fattest class [5, 9, 12]


collision-avoiding layer 2: m=93 of ceiling 96; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [0, 9, 13]


collision-avoiding layer 2: m=92 of ceiling 96; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [7, 8, 10, 14]


collision-avoiding layer 2: m=92 of ceiling 96; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [0, 13, 17]


collision-avoiding layer 2: m=107 of ceiling 108; chi=8=omega tracks the clique (DSATUR ub 8); fattest class [0, 14, 17]


collision-avoiding layer 2: m=106 of ceiling 108; chi=8=omega tracks the clique (DSATUR ub 8); fattest class [1, 5, 7]


collision-avoiding layer 2: m=106 of ceiling 108; chi=7=omega tracks the clique (DSATUR ub 7); fattest class [1, 4, 7, 12]


chi=10 proved twice: alpha<=2 covering bound (ceil(19/2)=10, alpha verified brute-force) and UNSAT at 9 colours (48 ms); omega=8 so chi-omega=2, K9-free. The union is forced; split search: SA best defect 28 over 55 iters/1 restarts in 75s; nonplanar: layer 1 K5, layer 2 K5. Exact B&B queued in background.


chi=10 proved twice: alpha<=2 covering bound (ceil(19/2)=10, alpha verified brute-force) and UNSAT at 9 colours (32 ms); omega=8 so chi-omega=2, K9-free. The union is forced; split search: SA best defect 26 over 60 iters/1 restarts in 75s; nonplanar: layer 1 K3,3, layer 2 K5. Exact B&B queued in background.


chi=10 proved twice: alpha<=2 covering bound (ceil(19/2)=10, alpha verified brute-force) and UNSAT at 9 colours (87 ms); omega=8 so chi-omega=2, K9-free. The union is forced; split search: SA best defect 27 over 58 iters/1 restarts in 75s; nonplanar: layer 1 K3,3, layer 2 K3,3. Exact B&B queued in background.


chi=10 proved twice: alpha<=3 covering bound (ceil(28/3)=10, alpha verified brute-force) and UNSAT at 9 colours (510 ms); omega=8 so chi-omega=2, K9-free. The union is forced; split search: SA best defect 53 over 20 iters/1 restarts in 90s; nonplanar: layer 1 K3,3, layer 2 K3,3. Exact B&B queued in background.


boundary: omega<=8 forces all adjacent sums <=8; Sigma=20 forces t=(4,4,4,4,4) (odd cycle equalizes); chi>=ceil(20/2)=10 by the covering bound but m=110 > 108 = 6n-12. Dead on the Euler ceiling by 2 edges - the closest infeasible member.


boundary: L=9 needs Sigma>=9*4+1=37 for chi>=10 but pair cap gives Sigma<=36; C9[K4] hits 36 and chi=9 exactly (SAT, clique 8 precoloured). In corridor (m=198<=204) but 9-colourable; SA split defect 69 (planar=[False, False]) - a chi=9 biplanar graph would only tie Sulanke, not beat it.


boundary: every C_n^k with k>=6 has m=kn > 6n-12 (here 114>102); infeasible for all n. k<=5 members are 9-colourable by arc partition unless complete (then contain K9).


densest in-corridor cycle power (m=85 in [77,90]): chi=9 exact by SAT, omega=6; k<=5 caps chi at k+1+ceil(k/2)<=9 (arc colouring), so the family cannot reach 10. SA split defect 20.


boundary: chi(K(n,k))=n-2k+2>=10 forces n>=2k+8, so degree C(n-k,k) >= C(k+8,k) >= 45 for k>=2, but biplanar average degree < 12. K(12,2): n=66, m=1485 >> 384 = 6n-12. k=1 gives K_n containing K9 (f004). Full Kneser graphs are all dead; their sparse chi-critical SUBGRAPHS (Schrijver etc.) stay open.


boundary: S(n) has avg degree 2(n-2)/3 > 12 - eps for n>=20 (m=1140 > 1128 = 6N-12 at n=20, and the ratio only grows), while chi = ceil(log2 n) >= 10 needs n >= 513. The corridor caps full shift graphs at n<=19 where chi<=5. Dead.


union of two stacked quadrangulations, n=20

boundary: two triangle-free planar layers carry at most 2(2n-4) = 4n-8 edges (here m=36 <= 72), strictly below the criticality floor ceil(9n/2)=90. The whole family is infeasible at every n; see the triangle constraint finding.


complement of triangle-free Gbar n=19 m=69 alpha=8

alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 006ebd7cc4dc; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


complement of triangle-free Gbar n=19 m=70 alpha=8

alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 00f04e46f976; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 04c22789e997; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 051f76f7619a; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 05981668cf6e; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 073ea4803511; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 09eac4ca9a66; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 0a4176264bed; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


complement of triangle-free Gbar n=19 m=71 alpha=8

alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 0aaf863678c7; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 0b02de8bf21e; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 0c63e1b00e8e; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 0c83038f2b12; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 0d475e78a235; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 0e1769ced381; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 0e7a6ac5963e; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 0e7fae961e14; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 0fde8567d2b4; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 102128b59fdc; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 13255d92670b; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 13b43bf81028; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 13d78190420c; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 174c9b794401; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 19a93878e66b; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 1a2273a19f62; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 1a79892de00c; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 68 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 1ab0f988da58; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 1ab5a4b08159; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 1adbd0170237; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 1ce88a68b4ab; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 1dac1d62d6f6; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 68 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 1dd6c9387242; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 1df8bb9240e9; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 1e2d73b54cf9; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 20577bf11d7a; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 21733302adc9; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 217e050827c1; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 22febe4fd1a5; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 2331ff3ad7c2; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 23c2443a5de6; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


complement of triangle-free Gbar n=19 m=72 alpha=8

alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL 25abb1c9fb15; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 26d325048ab2; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 2703c14ea76b; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 2873406ffa1f; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 28890ebe2aa2; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 28c486948f70; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 29436a01434f; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 29a4dc3b1e90; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 29e56fb1bc78; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 2add745f7b56; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 2c1e5fc92bf4; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 2c81e6894534; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 2d04281237a6; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 2e8a31e91194; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 68 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 30e0ed66cfa3; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 3134509a1b3d; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 3287f014308a; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 339564ea6093; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 33a86775c26a; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 34071bfc9a6c; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 34187a5a42f8; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 351eabe7429b; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 36fb2b4dbc01; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL 37e8a2a905dc; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 38bde98450c5; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 3937dccb7cdc; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 67 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 3c7ca5b43b42; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 3e1bbd1e7d00; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 3e53e966bab9; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 4063fc00f177; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 67 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 438566c17b9e; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 45429c96057f; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 4546627805c3; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 498701952ad0; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 49aaf703f9f0; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL 4b6e03079849; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 507c63a98aff; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 51974b547341; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 52059865012c; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 520b4684daa4; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 57dcf52dc78e; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 5822f11540f6; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 583ca26ddec1; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 584dc9736bbc; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 58ff6d93bc86; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 5961e425f2c0; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 5a64b304455c; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 5aae9d75d308; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 5c279190f844; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 5c7c47beeade; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 5ca4d28d4c51; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 5d156e0d3a18; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 5d3ae334cd14; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 5ed22dde26e8; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 5f2f33b7291b; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 6036cd5876e4; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 634531268282; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 650cb944d344; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 65337ed81242; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 655e1b141d39; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 6669ad76707d; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 68 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 66c60b66d06a; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 6816fd71e1a7; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 71 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 68a9a6bc9c95; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 6ae017400d28; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 6ae936393e56; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 6b9fbe5a192e; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 6c19043b8b48; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 6cdfd1ed6b89; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 6de7bd08aa48; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 6e39f8bd01a4; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 6e3f94a6ba08; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 6ebb61c3d5b4; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 7061ecbc1c32; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 71c884f32045; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 72ad0cf446aa; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 7536ec23c10b; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 76432c0d7b7a; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 7855c9aa5c11; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 789d30cdc673; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 78e93fecc77e; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 78f9db688f43; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 7a23007ce4ca; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 7b8428b0c757; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 7d7686e4560c; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 7d9252d3a79d; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 7e6369329158; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 8078ca422d9b; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 80872bd98c82; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 80d7c85e5d15; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 81058c93edcb; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 81bc9dd0b4ec; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 81c976420029; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 81f430cfce93; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 83dbc738daf9; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 844b720f222c; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 8621696b156b; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 87e15b875d36; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 8a1e72ef458e; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 8a1fd53eb386; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 8a37a541336e; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 8bbd9b4c34e2; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 8c078ddf0698; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 8d7c2e647aaf; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 8daa114e803e; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 8f607d3b1002; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 908a38c04692; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 917321bbf63d; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 918a90d2790b; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 91af9d610c5d; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 923be4a7a626; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 925636c38dd5; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 67 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 928910ea3639; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 92ec43456684; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 934d911301a4; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 9529aac81ddf; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 95572508a167; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 956a6edbbd2c; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 981f2e355a42; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 993d7fde5b27; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 9a4a322702ad; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 9a9c29fd7b99; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 9aca5a6233df; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 9d15be56cf1d; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 9d440a0d562a; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL 9dd4f6a790d6; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 9e4198185b78; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 9f38fa029705; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 9f5390da2cba; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL 9f966e692aa3; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL 9ff32891ecc4; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL a06aab31f03b; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL a0845f81333c; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL a0948682d6a6; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL a10db4062de4; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL a1604e5b09cd; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL a3a6c7ad7ced; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL a658756f49b4; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL a814cf237062; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL ab7408163a3a; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL ab8ccdec7034; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL abb140c5a3cb; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL abeb31ec8eec; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL acb021c01df2; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 68 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL ae8ea0016456; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 68 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL b07675aa7a82; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL b0e0aab7f895; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL b0f53e85bdc5; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL b14a8bcf0189; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL b23b95db68d2; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL b307ffa8f290; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 71 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL b400d4101cc0; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL b55361c8d1af; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL b5a20949e815; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL b5c0aaff44a2; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL b67757eeacac; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL b90590494cba; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL b9c71afab345; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL ba3154c93196; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL bae13c4f31aa; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL bb980df0e6d2; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL bcc028e9ce49; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL bde0227eee8f; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL becb7c834912; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL bef977c469e4; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL bf6569ee38e6; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL c0a4df41107d; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 71 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL c1bcf8040804; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL c1e295450380; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL c1ebe6a9c118; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL c3a3c07ec835; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL c3ec76da7402; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL c5ead8af33ad; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL c6cd738b3b8c; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL c802489960e3; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL c86dab54ad84; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL c8c603de5952; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL c9150235f692; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL c94fc04a0ef7; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL c96d32cbb537; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL cb105d85e62a; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL cbbb45158534; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL cbeaa7671e0a; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL cd3176b1f665; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL cd5ea0daf575; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL cd8253eabce1; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL cd9000f6aed9; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL d276d0b1c25c; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL d2de2f08ecf4; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL d2eb956c6ce0; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL d303d9b8fa64; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL d321eb41ac1d; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL d32eb95aa92a; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL d3e6a94fd818; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL d4edd2c207f3; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL d5e0c34bc452; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL d62dfd351439; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL d66e84631a0c; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL d68c483163e8; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL d6ccaec5017d; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL d6eb578faa04; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL d7b1c5352ce7; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL d81eab2846b3; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL d98902826bb7; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL d997dc325d84; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL d9cc3020b31f; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 68 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL da25c985d1b6; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL dac11e861c3c; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL db50fef990bd; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL dc2e045adbc4; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL dd0586656ef7; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL dd7425ab5b27; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL ddf57c7d01bf; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL deb09d665a3c; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL df83776a2291; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL dfaa6938246a; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL e143c6d2bf80; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL e15f50765e6c; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL e16caa500dc7; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL e3124953c9c6; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL e49ed8449167; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL e71c4d1a2ad3; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL e88c879bfa10; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL e9828c0438fc; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL ea5b274cf456; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL ead54d7c87b0; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL ebbb2217ddf1; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 71 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL ec02bcb5baeb; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 71 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL ec5956af3157; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL ee0d9e412d2d; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL eebe9d1e587e; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL efc8bb3fad29; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL efcc5eb18f06; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL f1c1c99668e7; found by seed 15): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL f46ebe18cf18; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL f49d747ae6f8; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL f4eceff28ae7; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL f5a0e7209518; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL f624fc6893a1; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 67 vs cap 68: SURVIVES heuristic screen - CEGAR-worthy


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL f6d4a78d8b1d; found by seed 11): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL f938d49c85d6; found by seed 13): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL fb22e869e5f6; found by seed 14): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL fb40139f760f; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL fb66ef0ec5d2; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL fc569c84bc6f; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL fcdce7314636; found by seed 16): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL fd4fed180c51; found by seed 1): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL fe5654edc2da; found by seed 12): complement has alpha=2 so chi>=10 (covering), omega<=8. non-blowup. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED - non-biplanar (certificate in params)


alpha-route candidate a00080, n=19 m=102 Euler-tight

run-06 closure row for a00080: properties re-verified fresh (complement triangle-free = alpha 2; omega=8<=8; chi>=10 by covering AND UNSAT@9 in 18ms). Euler-tight m=102 forces both layers to be 19-vertex triangulations; tight-CEGAR seeds (triangulation constraints + K5 + K33) are UNSAT at round 0 under both Glucose3 and Cadical: NOT biplanar. Independent recheck logged separately.


alpha-route candidate a00124, n=19 m=102 Euler-tight

run-06 closure row for a00124: properties re-verified fresh (complement triangle-free = alpha 2; omega=8<=8; chi>=10 by covering AND UNSAT@9 in 45ms). Euler-tight m=102 forces both layers to be 19-vertex triangulations; tight-CEGAR seeds (triangulation constraints + K5 + K33) are UNSAT at round 0 under both Glucose3 and Cadical: NOT biplanar. Independent recheck logged separately.


alpha-route candidate a00206, n=19 m=102 Euler-tight

run-06 closure row for a00206: properties re-verified fresh (complement triangle-free = alpha 2; omega=8<=8; chi>=10 by covering AND UNSAT@9 in 32ms). Euler-tight m=102 forces both layers to be 19-vertex triangulations; tight-CEGAR seeds (triangulation constraints + K5 + K33) are UNSAT at round 0 under both Glucose3 and Cadical: NOT biplanar. Independent recheck logged separately.


alpha-route candidate a00238, n=19 m=102 Euler-tight

run-06 closure row for a00238: properties re-verified fresh (complement triangle-free = alpha 2; omega=8<=8; chi>=10 by covering AND UNSAT@9 in 19ms). Euler-tight m=102 forces both layers to be 19-vertex triangulations; tight-CEGAR seeds (triangulation constraints + K5 + K33) are UNSAT at round 0 under both Glucose3 and Cadical: NOT biplanar. Independent recheck logged separately.


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL-hash 4b6e03079849): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 71c884f32045): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash 9d15be56cf1d): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash b88d94f3aca6): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash 6074f98b6ebb): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash 4c08dff50207): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 68 vs cap 68: inconclusive (heuristic LB only) - CEGAR-worthy


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash a10db4062de4): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 68 vs cap 68: inconclusive (heuristic LB only) - CEGAR-worthy


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash e9828c0438fc): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL-hash 25abb1c9fb15): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 102128b59fdc): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL-hash ab7408163a3a): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash deb09d665a3c): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash 6036cd5876e4): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash b9c71afab345): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash fb40139f760f): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL-hash 37e8a2a905dc): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 174c9b794401): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash 0c83038f2b12): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL-hash c94fc04a0ef7): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 68 vs cap 68: inconclusive (heuristic LB only) - CEGAR-worthy


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 7d7686e4560c): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 7536ec23c10b): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash f6d4a78d8b1d): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 3e53e966bab9): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 8bbd9b4c34e2): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 47658392c783): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 67 vs cap 68: inconclusive (heuristic LB only) - CEGAR-worthy


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash d68c483163e8): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 1df8bb9240e9): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash c539bb4cbe26): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 68 vs cap 68: inconclusive (heuristic LB only) - CEGAR-worthy


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash bcc028e9ce49): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash a10db4062de4): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash 6036cd5876e4): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 71c884f32045): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL-hash 25abb1c9fb15): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 09eac4ca9a66): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 1e2d73b54cf9): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 6e39f8bd01a4): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 68 vs cap 68: inconclusive (heuristic LB only) - CEGAR-worthy


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 04c22789e997): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash 8daa114e803e): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 81c976420029): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 9dd4f6a790d6): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 0e7fae961e14): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash ddf57c7d01bf): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 95572508a167): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash 8078ca422d9b): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 7d9252d3a79d): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 68 vs cap 68: inconclusive (heuristic LB only) - CEGAR-worthy


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 0b02de8bf21e): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 68 vs cap 68: inconclusive (heuristic LB only) - CEGAR-worthy


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash e16caa500dc7): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash 2a6da1994b7c): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash c6cd738b3b8c): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash d68c483163e8): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash f834c41abcef): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 0aaf863678c7): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL-hash 37e8a2a905dc): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 29a4dc3b1e90): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=70, alpha=8, triangle-free; WL-hash c96d32cbb537): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash efc8bb3fad29): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 72 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=69, alpha=8, triangle-free; WL-hash ce8a567afbcc): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=71, alpha=8, triangle-free; WL-hash 51974b547341): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 70 vs cap 68: KILLED by f025 - non-biplanar


alpha-route hit (Gbar: m=72, alpha=8, triangle-free; WL-hash 4b6e03079849): complement has alpha=2 so chi>=ceil(19/2)=10, omega=8<=8. NOT a C5-blowup: new structure. f025 screen: max triangle-free subgraph >= 69 vs cap 68: KILLED by f025 - non-biplanar